Heterojunction

A heterojunction is the interface that occurs between two layers or regions of dissimilar crystallinesemiconductors. These semiconducting materials have unequal band gaps as opposed to a homojunction. It is often advantageous to engineer the electronic energy bands in many solid-state device applications, including semiconductor lasers, solar cells and transistors ("heterotransistors") to name a few. The combination of multiple heterojunctions together in a device is called a heterostructure, although the two terms are commonly used interchangeably. The requirement that each material be a semiconductor with unequal band gaps is somewhat loose, especially on small length scales, where electronic properties depend on spatial properties. A more modern definition of heterojunction is the interface between any two solid-state materials, including crystalline and amorphous structures of metallic, insulating, fast ion conductor and semiconducting materials.

The three types of semiconductor heterojunctions organized by band alignment.

Band diagram for straddling gap, n-n semiconductor heterojunction at equilibrium.

The behaviour of a semiconductor junction depends crucially on the alignment of the energy bands at the interface.
Semiconductor interfaces can be organized into three types of heterojunctions: straddling gap (type I), staggered gap (type II) or broken gap (type III) as seen in the figure.[citation needed]
Away from the junction, the band bending can be computed based on the usual procedure of solving Poisson's equation.

Various models exist to predict the band alignment.

The simplest (and least accurate) model is Anderson's rule, which predicts the band alignment based on the properties of vacuum-semiconductor interfaces (in particular the vacuum electron affinity). The main limitation is its neglect of chemical bonding.

A common anion rule was proposed which guesses that since the valence band is related to anionic states, materials with the same anions should have very small valence band offsets. This however did not explain the data but is related to the trend that two materials with different anions tend to have larger valence band offsets than conduction band offsets.

The 60:40 rule is a heuristic for the specific case of junctions between the semiconductor GaAs and the alloy semiconductor AlxGa1−xAs. As the x in the AlxGa1−xAs side is varied from 0 to 1, the ratio ΔEC/ΔEV{\displaystyle \Delta E_{C}/\Delta E_{V}} tends to maintain the value 60/40. For comparison, Anderson's rule predicts ΔEC/ΔEV=0.73/0.27{\displaystyle \Delta E_{C}/\Delta E_{V}=0.73/0.27} for a GaAs/AlAs junction (x=1).[5][6]

The typical method for measuring band offsets is by calculating them from measuring exciton energies in the luminescence spectra.[6]

When a heterojunction is formed by two different semiconductors, a quantum well can be fabricated due to difference in band structure. In order to calculate the static energy levels within the achieved quantum well, understanding variation or mismatch of the effective mass across the heterojunction becomes substantial. The quantum well defined in the heterojunction can be treated as a finite well potential with width of lw{\displaystyle l_{w}}. Addition to that, in 1966, Conley et al.[7] and BenDaniel and Duke[8] reported boundary condition for the envelope function in quantum well, known as BenDaniel-Duke boundary condition. According to them, the envelope function in fabricated quantum well must satisfy boundary condition which states ψ(z),1m∗∂∂zψ(z){\displaystyle \psi (z),{\frac {1}{m^{*}}}{\partial \over {\partial z}}\psi (z)\,} are both continuous in interface regions.

Image of a nanoscale heterojunction between iron oxide (Fe3O4 — sphere) and cadmium sulfide (CdS — rod) taken with a TEM. This staggered gap (type II) offset junction was synthesized by Hunter McDaniel and Dr. Moonsub Shim at the University of Illinois in Urbana-Champaign in 2007.

In quantum dots the band energies are dependent on crystal size due to the quantum size effects. This enables band offset engineering in nanoscale heterostructures. It is possible[10] to use the same materials but change the type of junction, say from straddling (type I) to staggered (type II), by changing the size or thickness of the crystals involved. The most common nanoscale heterostructure system is ZnS on CdSe (CdSe@ZnS) which has a straddling gap (type I) offset. In this system the much larger band gap ZnS passivates the surface of the fluorescent CdSe core thereby increasing the quantum efficiency of the luminescence. There is an added bonus of increased thermal stability due to the stronger bonds in the ZnS shell as suggested by its larger band gap. Since CdSe and ZnS both grow in the zincblende crystal phase and are closely lattice matched, core shell growth is preferred. In other systems or under different growth conditions it may be possible to grow anisotropic structures such as the one seen in the image on the right.

It has been shown[11] that the driving force for charge transfer between conduction bands in these structures is the conduction band offset. By decreasing the size of CdSe nanocrystals grown on TiO2, Robel et al.[11] found that electrons transferred faster from the higher CdSe conduction band into TiO2. In CdSe the quantum size effect is much more pronounced in the conduction band due to the smaller effective mass than in the valence band, and this is the case with most semiconductors. Consequently, engineering the conduction band offset is typically much easier with nanoscale heterojunctions. For staggered (type II) offset nanoscale heterojunctions, photoinduced charge separation can occur since there the lowest energy state for holes may be on one side of the junction whereas the lowest energy for electrons is on the opposite side. It has been suggested[11] that anisotropic staggered gap (type II) nanoscale heterojunctions may be used for photocatalysis, specifically for water splitting with solar energy.

Feucht, D. Lion; Milnes, A.G. (1970). Heterojunctions and metal-semiconductor junctions. New York City and London: Academic Press., ISBN0-12-498050-3. A somewhat dated reference respect to applications, but always a good introduction to basic principles of heterojunction devices.